Question

# If $$AB = 12$$ cm, $$BC = 16$$ cm and $$AB$$ is perpendicular to $$BC$$, then the radius of the circle passing through the points $$A$$, $$B$$ and $$C$$ is:

A
6 cm
B
8 cm
C
10 cm
D
12 cm

Solution

## The correct option is C $$10\ cm$$Given- $$A, B$$ &  $$C$$ are points such that $$AB=12cm$$ and $$BC=16cm$$  and $$BC\bot AB$$. To find out- the radius of the circle passing through $$A, B$$ &  $$C=?$$ Solution- $$BC\bot AB$$ i.e $$\angle ABC={ 90 }^{ 0 }$$ and $$\Delta ABC$$ is a right one with $$AC$$ as hypotenuse. $$\therefore AC=\sqrt { { AB }^{ 2 }+{ BC }^{ 2 } } =\sqrt { { 12 }^{ 2 }+{ 16 }^{ 2 } } cm=20cm$$. So the circle passing through $$A, B$$ &  $$C$$ will have its  diameter as $$AC$$. $$\therefore$$  Its radius$$=\dfrac { 1 }{ 2 } \times 20cm=10cm.$$ Ans- Option C.Mathematics

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